Question

Find which of the following discount series is better for the customer:
(i) $30\% ,20\% ,{\rm{ and 10\% }}$ ;
(ii) $25\% ,20\% ,{\rm{ and 15\% }}$ .

Answer 1

Hint: In this question two successive discount series are given and we have to find out which one of these series is better for the customer. We know that whichever discount series gives the lowest selling cost for the customer will be the better option for the customer. So, we calculate the final selling price of the first series and then compare with the selling price of the second series. The discount series having lower value of selling price would be our answer.

Complete step-by-step answer:
Given:
Let us assume the Marked Price (M.P.) is ${\rm{Rs}}{\rm{. 100}}$ .
(i) The given discount series is - $30\% ,20\% ,{\rm{ and 10\% }}$
So, the first Discount Price (D.P.) is given by –
$
\Rightarrow {\rm{D}}{{\rm{P}}_1} = 30\% {\rm{ of MP}}\\
\Rightarrow {\rm{D}}{{\rm{P}}_1} = \dfrac{{30}}{{100}} \times 100\\
\Rightarrow {\rm{D}}{{\rm{P}}_1} = {\rm{Rs}}{\rm{. 30}}
$
Then, the selling price after the first discount of 30% can be calculated by –
$
\Rightarrow {\rm{S}}{{\rm{P}}_1}{\rm{ = MP - D}}{{\rm{P}}_1}\\
\Rightarrow {\rm{S}}{{\rm{P}}_1}{\rm{ = }}100 - 30\\
\Rightarrow {\rm{S}}{{\rm{P}}_1}{\rm{ = Rs}}{\rm{. }}70
$
Now this selling price would be the marked price for the next discount. So,
The second Discount Price (D.P.) is given by –
$
\Rightarrow {\rm{D}}{{\rm{P}}_2} = 20\% {\rm{ of S}}{{\rm{P}}_1}\\
\Rightarrow {\rm{D}}{{\rm{P}}_2} = \dfrac{{20}}{{100}} \times 70\\
\Rightarrow {\rm{D}}{{\rm{P}}_2} = {\rm{Rs}}{\rm{. 14}}
$
Then, the selling price after the second discount of 20% can be calculated by –
$
\Rightarrow {\rm{S}}{{\rm{P}}_2}{\rm{ = S}}{{\rm{P}}_1}{\rm{ - D}}{{\rm{P}}_2}\\
\Rightarrow {\rm{S}}{{\rm{P}}_2}{\rm{ = 70}} - 14\\
\Rightarrow {\rm{S}}{{\rm{P}}_2}{\rm{ = Rs}}{\rm{. 56}}
$
And now this selling price would be the marked price for the next discount. So,
The third Discount Price (D.P.) is given by –
$
\Rightarrow {\rm{D}}{{\rm{P}}_3} = 10\% {\rm{ of S}}{{\rm{P}}_2}\\
\Rightarrow {\rm{D}}{{\rm{P}}_3} = \dfrac{{10}}{{100}} \times 56\\
\Rightarrow {\rm{D}}{{\rm{P}}_3} = {\rm{Rs}}{\rm{. 5}}{\rm{.6}}
$
Then, the selling price after the third discount of 10% can be calculated by –
$
\Rightarrow {\rm{S}}{{\rm{P}}_3}{\rm{ = S}}{{\rm{P}}_2}{\rm{ - D}}{{\rm{P}}_3}\\
\Rightarrow {\rm{S}}{{\rm{P}}_3}{\rm{ = 56}} - 5.6\\
\Rightarrow {\rm{S}}{{\rm{P}}_3}{\rm{ = Rs}}{\rm{. 50}}{\rm{.4}}
$
So, the final selling price of the first discount series is ${\rm{Rs}}{\rm{. 50}}{\rm{.4}}$.

(ii) The given discount series is - $25\% ,20\% ,{\rm{ and 15\% }}$
So, the first Discount Price (D.P.) is given by –
$
\Rightarrow {\rm{D}}{{\rm{P}}_1} = 25\% {\rm{ of MP}}\\
\Rightarrow {\rm{D}}{{\rm{P}}_1} = \dfrac{{25}}{{100}} \times 100\\
\Rightarrow {\rm{D}}{{\rm{P}}_1} = {\rm{Rs}}{\rm{. 25}}
$
Then, the selling price after the first discount of 25% can be calculated by –
$
\Rightarrow {\rm{S}}{{\rm{P}}_1}{\rm{ = MP - D}}{{\rm{P}}_1}\\
\Rightarrow {\rm{S}}{{\rm{P}}_1}{\rm{ = }}100 - 25\\
\Rightarrow {\rm{S}}{{\rm{P}}_1}{\rm{ = Rs}}{\rm{. }}75
$
Now this selling price would be the marked price for the next discount. So,
The second Discount Price (D.P.) is given by –
$
\Rightarrow {\rm{D}}{{\rm{P}}_2} = 20\% {\rm{ of S}}{{\rm{P}}_1}\\
\Rightarrow {\rm{D}}{{\rm{P}}_2} = \dfrac{{20}}{{100}} \times 75\\
\Rightarrow {\rm{D}}{{\rm{P}}_2} = {\rm{Rs}}{\rm{. 15}}
$
Then, the selling price after the second discount of 20% can be calculated by –
$
\Rightarrow {\rm{S}}{{\rm{P}}_2}{\rm{ = S}}{{\rm{P}}_1}{\rm{ - D}}{{\rm{P}}_2}\\
\Rightarrow {\rm{S}}{{\rm{P}}_2}{\rm{ = 75}} - 15\\
\Rightarrow {\rm{S}}{{\rm{P}}_2}{\rm{ = Rs}}{\rm{. 60}}
$
And now this selling price would be the marked price for the next discount. So,
The third Discount Price (D.P.) is given by –
$
\Rightarrow {\rm{D}}{{\rm{P}}_3} = 15\% {\rm{ of S}}{{\rm{P}}_2}\\
\Rightarrow {\rm{D}}{{\rm{P}}_3} = \dfrac{{15}}{{100}} \times 60\\
\Rightarrow {\rm{D}}{{\rm{P}}_3} = {\rm{Rs}}{\rm{. 9}}
$
Then, the selling price after the third discount of 10% can be calculated by –
$
\Rightarrow {\rm{S}}{{\rm{P}}_3}{\rm{ = S}}{{\rm{P}}_2}{\rm{ - D}}{{\rm{P}}_3}\\
\Rightarrow {\rm{S}}{{\rm{P}}_3}{\rm{ = 60}} - 9\\
\Rightarrow {\rm{S}}{{\rm{P}}_3}{\rm{ = Rs}}{\rm{. 51}}
$
So, the final selling price of the second discount series is ${\rm{Rs}}{\rm{. 51}}$.
Now comparing the final selling prices of both the discounted series (i) and (ii), we see that the value of final selling price of series (i) is less than the final selling price of series (ii) which means that the customer has to pay less cost price if he chooses series (i).
Therefore, the discount series (i) $30\% ,20\% ,{\rm{ and 10\% }}$ is better for customers.
So, the correct answer is “Option I”.

Note: It should be noted that the discount is always given on the marked price of the product. But in this case the successive discounts are given, so the marked price for the second discount would be the selling price after the first discount and similarly for the third discount the selling price after the second discount would be its marked price.